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Investing through Economic Cycles with EnsembleMachine Learning Algorithms

Thomas Raffinot

Silex Investment Partners

Big Data in Finance Conference

Thomas Raffinot (Silex-IP) Economic Cycles-Machine Learning Big Data in Finance 1 / 22

Turning points detection in real time: Ensemble MLalgorithms

In theory, investment strategies based on growth cycle turning pointsoutperform not only passive buy-and-hold benchmarks, but also busi-ness cycles’ strategies

Nowcasting growth cycle turning points in real time in the euro areaand in the United States to time markets

Non parametric model to avoid local maxima in the likelihood

Ensemble machine learning algorithms:I Random forest (Breiman (2001))I Boosting (Schapire (1990))




















Ensemble Machine Learning Algorithms

Machine learning adapts statistical methods to get better results in anenvironment with much more data and processing power

Ensemble algorithms: making decisions based on the input of multiplepeople or experts

Entertain a large number of predictors and perform estimation andvariable selection simultaneously

Random forest (Breiman (2001)): simple averaging of models

Boosting (Schapire (1990)): iterative process where the errors are keptbeing modelled






























Random forest

Each decision tree is built from a bootstrapped sample of the fulldataset and then, at each node, only a random sample of the availablevariables is usedAlgorithm:

I Given that a training set consists of N observations and M features,choose a number m ≤ M of features to randomly select for each treeand a number K that represents the number of trees to grow.

II Take a bootstrap sample Z of the N observations. So about two thirdof the cases are chosen. Then select randomly m features.

III Grow a CART using the bootstrap sample Z and the m randomlyselected features.

IV Repeat the steps 2 and 3, K times.V Output the ensemble of trees TK

1

VI For regression, to make a prediction at a new point x :

yRF (x) =1

K

K∑i=1

Ti (x)


The gradient descent view of boosting (Friedman (2001))

The task is to estimate the function f (x), that minimizes the expecta-tion of some loss function, Ψ(y , f ), i.e.,

f (x) = arg minf (x)

E(Ψ(y , f (x))

One has to provide the choices of functional parameters Ψ(y , f ) andthe weak learner h(x, θ)

The function estimate f (x) is parameterized in the additive functionalform:

f (x) =

Mstop∑m=1

βmh(x, θm)

The original function optimization problem has thus been changed toa parameter optimization problem

The size of the ensemble is determined by M, which is determined bycross-validation


Boosting: loss-functions

The most frequently used loss-functions for classification are the fol-lowing:

I y typically takes on binary values y ∈ 0, 1. To simplify the notation, letus assume the transformed labels y = 2y − 1 making y ∈ −1, 1

I Adaboost loss function: Ψ(y , f (x)) = exp(−y f (x))I Binomial loss function: Ψ(y , f (x)) = − log(1 + exp(−2y f (x)))

The most frequently used loss-functions for regression are the following:

I Squared error loss: Ψ(y , f (x)) = (y − f (x))2

I Absolute loss: Ψ(y , f (x)) = |y − f (x|


GBM algorithm with shrinkage

Step 1 Initialize f0(x) = arg minρ∑N

i=1 Ψ(yi , ρ),m = 0.

Step 2 m = m + 1

Step 3 Compute the negative gradient

zi = −∂

∂f (xi )Ψ(yi , f (xi ))|

f (xi )=fm−1(xi )

, i = 1, . . . , n

Step 4 Fit the base-learner function, h(x, θ) to be the most correlated with the gradient vector.

θm = arg minβ,θ

n∑i=1

zi − βh(xi , θm)

Step 5 Find the best gradient descent step-size ρm

ρm = arg minρ

N∑i=1

Ψ(yi , f (xi )m−1 + ρh(x, θm))

Step 6 Update the estimate of fm(x) as

fm(x)← f (x)m−1 + λρmh(x, θm))

Step 7 Iterate 2-6 until m = Mstop .


Variables: almost non-revised series

Financial series:Government bonds, Yield curves, investment-grade and high-yield cor-porate spreads, stock markets (Large caps, large caps sectors, smallcaps, mid caps, the growth and value version of those indexes), Assetsvolatility, VIX index and the VSTOXX index, commodities (crude oil,natural gas, gold, silver and CRB index),...

Economic surveys:European Commission, the Institute for Supply Management, the Con-ference Board and the National Association of Home Builders (NAHB)

Real economic data:Initial claims

Different lags of differentiation were considered: 1 to 18 months

More than 1000 variables


Different models

Boosting:I Combination of a binomial loss function with decision trees (”BTB”) as

in Ng (2014)I Combination of a squared error loss function with P-splines (”SPB”) as

in Berge (2015) or Taieb et al. (2015)

Random forest RF

Competitive models:I Acc classifies all data as ”acceleration”I Slow classifies all data as ”slowdown”I Random randomly assigns classes based on the proportions found in the

training dataI Prob refers to the probit model based on the term spreadI MS refers to the Markov-switching dynamic factor modelI EN refers to the elastic-net logistic model


Real time issues

To implement the ensemble algorithms, a classification of economicregimes is needed

Applied to the context of nowcasting, it can be summarized as follows:

Rt =

{1, if in acceleration

0, otherwise

A recursive estimation is computed:The ensemble algorithms are trained each month on a sample thatextends from the beginning of the sample through month T − 12, overwhich the turning point chronology is assumed known

The estimation windows is thus expanding as data accumulates, overthe period from January 2002 to December 2013


Data snooping

Data snooping occurs when a given set of data is used more than oncefor purposes of inference or model selection. It leads to the possibilitythat any successful results may be spurious because they could be dueto chance (White (2000))

Model Confidence Set (Hansen et al. (2011)): Model selection algo-rithm, which filters a set of models from a given entirety of models.The MCS aims at finding the best model and all models which areindistinguishable from the best


Classical criteria

The Brier’s Quadratic Probability Score (QPS):

QPS =1

F

F∑t=1

(yt − yt)2

The Area Under the ROC curve (AUROC), defined by:

AUROC =

∫ 1

0ROC(α)dα

where the Receiver Operating Characteristics (ROC) curve describes all possible combinations of true positive (Tp(c))and false positive rates (Fp(c)) that arise as one varies the threshold c used to make binomial forecasts from a real-valuedclassifier. As c is varied from 0 to 1, the ROC curve is traced out in (Tp(c), Fp(c)) space that describes the classificationability of the model.


Investment strategies

Disconnection between econometric predictability and actual profitabil-ity (Cenesizoglu and Timmermann (2012))

Very basic investment strategies:I Equity portfolio: if acceleration: 120% of his wealth is invested on the

asset and 20% of cash is borrowed, otherwise 80% of his wealth is in-vested on the asset and 20% is kept in cash

I Asset allocation; if acceleration: 80% of the portfolio is allocated toequities and 20% to bonds, otherwise 40% of the portfolio is allocatedto equities and 60% to bonds


Classical evaluation criteria in the United States, January2002 to December 2013

QPS AUROC

SPB 0.13RF 0.07∗∗ 0.94BTB 0.05∗∗ 0.94Prob 0.22MS 0.21EN 0.18Acc 0.21Slow 0.79Random 0.25

Note: ** indicates the model is in the set of best models M∗75%.


Turning point signals of the reference cycle in the UnitedStates

SPB RF BTB

Trough: February 2003 0 -1 -2Peak: October 2007 1 -2 -1Trough: September 2009 1 2 3Peak: June 2011 - 3 2Trough: December 2011 1 1

Note: Value shown is the model-implied peak/trough calculated using a 0.5 threshold. The minus sign refers to the leadin which the models anticipate the turning point dates. ”-” indicates that the model did not generate any signal. SPBrefers to a boosting model based on squared error loss with P-splines, RF refers to a random forest model, BTB refers toa boosting model based on binomial loss function with decision trees.


United States: 120/80 equity strategy, January 2002 toDecember 2013

Average returns Volatily SR MDDSPB 0.110 0.149 0.74∗∗ -0.43RF 0.107 0.147 0.72 -0.43BTB 0.109 0.146 0.75∗∗ -0.44Prob 0.094 0.173 0.54 -0.57MS 0.101 0.171 0.59 -0.56EN 0103 0.161 0.64 -0.51Acc 0.099 0.177 0.56 -0.58Slow 0.066 0.118 0.56 -0.43Random 0.092 0.155 0.59 -0.51Benchmark 0.083 0.147 0.56 -0.51



United States: dynamic asset allocation, January 2002 toDecember 2013

Average returns Volatily SR MDDSPB 0.091 0.090 1.0∗∗ -0.18RF 0.088 0.088 0.98 -0.18BTB 0.091 0.087 1.0∗∗ -0.20Prob 0.074 0.113 0.66 -0.39MS 0.075 0.101 0.74 -0.28EN 077 0.098 0.79 -0.25Acc 0.075 0.116 0.65 -0.42Slow 0.060 0.058 1 -0.18Random 0.076 0.095 0.79 -0.30Benchmark 0.068 0.085 0.79 -0.31



Classical evaluation criteria in the euro area, January 2002to December 2013

QPS AUROC

SPB 0.12∗∗ 0.90RF 0.11∗∗ 0.91BTB 0.12∗∗ 0.90Prob 0.25MS 0.20EN 0.15Acc 0.45Slow 0.54Random 0.48



Turning point signals of the reference cycle in the euro area

SPB RF BTB

Trough: September 2003 1 1 0Peak: May 2004 11 9 10Trough: May 2005 4 3 4Peak: October 2007 -1 1 -2Trough: August 2009 1 3 2Peak: June 2011 -1 -2 -2Trough: March 2013 2 2 3

Note: Value shown is the model-implied peak/trough calculated using a 0.5 threshold. The minus sign refers to the leadin which the models anticipate the turning point dates. ”-” indicates that the model did not generate any signal. SPBrefers to a boosting model based on squared error loss with P-splines, RF refers to a random forest model, BTB refers toa boosting model based on binomial loss function with decision trees.


Euro area: 120/80 equity strategy, January 2002 toDecember 2013

Average returns Volatily SR MDDSPB 0.085 0.161 0.53∗∗ -0.46RF 0.083 0.160 0.52∗∗ -0.46BTB 0.079 0.158 0.50 -0.46Prob 0.075 0.182 0.41 -0.48MS 0.076 0.178 0.43 -0.47EN 078 0.169 0.46 -0.47Acc 0.077 0.207 0.37 -0.61Slow 0.051 0.138 0.37 -0.43Random 0.076 0.182 0.42 -0.53Benchmark 0.064 0.173 0.37 -0.54



Euro area: dynamic asset allocation, January 2002 toDecember 2013

Average returns Volatily SR MDDSPB 0.081 0.094 0.86∗∗ -0.21RF 0.080 0.093 0.86∗∗ -0.22BTB 0.075 0.091 0.83 -0.22Prob 0.064 0.114 0.56 -0.25MS 0.069 0.105 0.66 -0.24EN 071 0.098 0.72 -0.23Acc 0.060 0.137 0.44 -0.44Slow 0.052 0.070 0.75 -0.21Random 0.064 0.115 0.55 -0.32Benchmark 0.06 0.100 0.55 -0.34



Conclusion

Timing the market based on the indicators is possible in real time

Ensemble machine learning algorithms are effective

Depending on the data and the objective, random forest sometimesperforms better than boosting, sometimes not

Further work:I Economic turning points forecasting (business cycles ?)I New features (google trends, news-based sentiment values,...)I Deep learning


Appendix: Correlations between lagged variables


References I

Berge, T. (2015). Predicting Recessions with Leading Indicators: ModelAveraging and Selection over the Business Cycle. Journal of Forecasting,34(6):455–471.

Breiman, L. (2001). Random forests. Machine Learning, 45:5–32.

Cenesizoglu, T. and Timmermann, A. (2012). Do return prediction modelsadd economic value? Journal of Banking and Finance, 36(11):2974 –2987. International Corporate Finance Governance Conference.

Friedman, J. H. (2001). Greedy function approximation: A gradient boostingmachine. The Annals of Statistics, 29:1189–1232.

Hansen, P., Lunde, A., and Nason, J. (2011). The model confidence set.Econometrica, 79(2):453–497.

Ng, S. (2014). Viewpoint: Boosting recessions. Canadian Journal of Eco-nomics, 47(1):1–34.


References II

Schapire, R. E. (1990). The strength of weak learnability. In MachineLearning, pages 197–227.

Taieb, S. B., Huser, R., Hyndman, R. J., and Genton, M. G. (2015). Prob-abilistic time series forecasting with boosted additive models: an applica-tion to smart meter data. Technical report.

White, H. (2000). A Reality Check for Data Snooping. Econometrica,68(5):1097–1126.


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